Margin of Error Calculator
You have your responses — this tells you how much to trust them. Enter your sample size and the result you observed, and see the range the true value plausibly falls within.
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Margin of error at 95% confidence.
If 50% of your 400 respondents chose an option, the true value is between 45.1% and 54.9%, 95 times out of 100.
How margin of error is calculated
MOE = z × √(p(1−p) ÷ n), expressed in percentage points.
z comes from your confidence level: 1.96 for 95%, 1.645 for 90%, 2.576 for 99%.
p = 50% is the default because it produces the widest margin. If your actual result is far from 50%, the real margin is narrower than the headline figure.
When you supply a population size, the finite population correction √((N − n) ÷ (N − 1)) is applied — it matters once your sample is more than about 5% of the population.
Questions people ask
What does a ±5% margin of error mean?
If 60% of respondents chose an option and the margin is ±5%, the true figure is between 55% and 65% at your stated confidence level. It does not mean the result is wrong by 5%.
Why is a 50% result the worst case?
Because p(1−p) peaks at p = 0.5. A result of 90% or 10% carries a smaller margin than a result of 50% at the same sample size.
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